Squarefree Integers And Extreme Values Of Some Arithmetic Functions

TL;DR

This paper investigates the behavior of the Dedekind psi function, showing that its extreme values occur at primorial integers and establishing a lower bound inequality for large primorials.

Contribution

It identifies the subset of primorial integers where the Dedekind psi function attains extreme values and proves a growth inequality for large primorials.

Findings

Extreme values of the Dedekind psi function occur at primorial integers.

The inequality psi(N_k) > c * loglog N_k holds for all large primorial integers.

Primorial integers support the extremal behavior of certain arithmetic functions.

Abstract

A study of the Dedekind psi function concludes that its extreme values are supported on the subset of primorial integers N_k = 2*3***p_k, where p_k is the kth prime. In particular, the inequality psi(N_k) > cloglogN_k, c > 0 constant, holds for all large primorial integers.